Queueing networks with a single shared server: light and heavy traffic

Authors:
M. A.A. Boon;R. D. van der Mei;E. M.M. Winands
Affiliations:
Eindhoven University of Technology, Eindhoven, The Netherlands;Centre for Mathematics and Computer Science (CWI), Department of Probability and Stochastic Networks, Amsterdam, The Netherlands;Department of Mathematics, Section Stochastics, VU University, Amsterdam, The Netherlands
Venue:
ACM SIGMETRICS Performance Evaluation Review - Special Issue on IFIP PERFORMANCE 2011- 29th International Symposium on Computer Performance, Modeling, Measurement and Evaluation
Year:
2011

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Abstract

We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems and robotics. Special cases of the introduced network include well-known polling models and tandem queues. We derive exact limits of the mean delays under both heavy-traffic and light-traffic conditions. By interpolating between these asymptotic regimes, we develop simple closed-form approximations for the mean delays for arbitrary loads.